real analysis - sup of Norm equals sup of inner product - Mathematics Stack Exchange
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SOLVED: Let M:[a, b] →𝐑^n × m be a continuous n × m-matrix-valued function, and let X=C([a, b], 𝐑^m) and Z=C([a, b], 𝐑^n) endowed with the supremum norm. Define the linear operator
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functional analysis - $\sup$ norm of a function - Mathematics Stack Exchange